Problem 139 Summary

[Lord_Farin]

I have not yet solved this problem, but I think I know the intention of the statement, however in my opinion there is some sort of grammar flaw in
"Finding Pythagorean triangles which allow the square on the hypotenuse square to be tiled."

I suggest it to be changed into "which allow the hypotenuse square to be tiled by the center square" or something with the same meaning. It is now like the middle square needs to be tiled, though it actually IS the tile used.

[elendiastarman]

You're right; there IS a bit of redundancy and ambiguity there. Your rephrasing is good and works...nothing more I can add... nice job!

[Lord_Farin]

Happy to help, after all, solving problems should not be about understanding questions grammatically, but mathematically

[Lord_Farin]

It seems that, after transferring to the new server, some setting has went wrong, creating problems like
263 An engineers’ dream come true

This clearly originates from a PHP problem since this text is literal in the HTML code. So I think you should convert the special characters to their HTML entity codes in PHP, that should solve the issue.

[hk]

I think I fixed the issues.
In case of any more issues of the issues returning please PM me.

[Lord_Farin]

It's now been a week, the problem summary hasn't been updated... Someone forgot in the chaos around the server transfer?

[hk]

Thanks.
I changed it in "Finding Pythagorean triangles which allow the square on the hypotenuse to be tiled." as in the summary there is no central square to be seen. That follows from the full description.

[Raman]

I don't understand this question quite clearly at all.
Could someone please elaborate upon that further?

Should the length of hypotenuse (c) be a multiple of that side of central square (|a-b|)?
If so, I actually get up with only 10 such right angled triangles.
4 3 5
20 21 29
120 119 169
696 697 985
4060 4059 5741
23660 23661 33461
137904 137903 195025
803760 803761 1136689
4684660 4684659 6625109
27304196 27304197 38613965

Raman.png

[Raman]

OK. Solved that. No more problems with that problem at all!

[Lord_Farin]

Despite your problem being solved, I kindly attend you to the fact that this is not about the problems semantics and understanding. Rather, it is about formulation and syntaxis. Therefore, in the future please refer to the problems section for questions.

[theos]

It would be quite helpful to note that triangles with their catheti swapped do not count extra, i.e. a < b.
e.g. {3,4,5} and {4,3,5} count only as one, even though they're, well, different triangles.

[hk]

It would be quite helpful to note that triangles with their catheti swapped do not count extra, i.e. a < b.
e.g. {3,4,5} and {4,3,5} count only as one, even though they're, well, different triangles.

Are they? In my view they are congruent. http://en.wikipedia.org/wiki/Congruence_(geometry)

[theos]

Admittedly, from a mathematical point of view it is not necessary.
Yet, for me as technician, it was not immediately obvious, especially when combined with the fact that there was no intermediate solution available either.